Coherence and Concentration in Tightly-Connected Networks
Coherence and Concentration in Tightly-Connected Networks
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紧密连接网络中的一致性和集中度
DOI：
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Enrique Mallada
中科院分区：
文献类型：
--
作者：
Hancheng Min;Enrique Mallada
在网络系统上实现协调行为的能力（工程或紧急）在几个领域引起了广泛的兴趣。这种兴趣已经导致了显着的进步，在发展的理论理解的条件下，网络内的代理可以达成协议（共识）或开发协调的行为，如同步。然而，人们对网络连贯性的理解要少得多。网络一致性通常是指网络中的节点具有相似的动态响应的能力，尽管它们的个体行为具有异质性。在本文中，我们开发了一个通用的框架来分析和量化的网络一致性的水平，一个系统表现出相关的系统的低秩属性的一致性。更准确地说，对于一个网络系统的线性动力学和耦合，我们表明，随着网络连接的增长，系统的传递矩阵收敛到一个秩一的传递矩阵表示的相干行为。有趣的是，这种秩为1的矩阵的非零特征值由单个节点动力学的调和平均给出，我们称之为相干动力学。我们的分析揭示了频率依赖性的一致性和动力学和网络拓扑结构之间的非平凡的相互作用。我们进一步表明，许多网络系统可以表现出类似的一致性行为，通过建立一个浓度的结果与随机选择的个人节点动态设置。
The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of the conditions under which agents within a network can reach an agreement (consensus) or develop coordinated behavior, such as synchronization. However, much less understood is the phenomenon of network coherence. Network coherence generally refers to nodes' ability in a network to have a similar dynamic response despite heterogeneity in their individual behavior. In this paper, we develop a general framework to analyze and quantify the level of network coherence that a system exhibits by relating coherence with a low-rank property of the system. More precisely, for a networked system with linear dynamics and coupling, we show that, as the network connectivity grows, the system transfer matrix converges to a rank-one transfer matrix representing the coherent behavior. Interestingly, the non-zero eigenvalue of such a rank-one matrix is given by the harmonic mean of individual nodal dynamics, and we refer to it as the coherent dynamics. Our analysis unveils the frequency-dependent nature of coherence and a non-trivial interplay between dynamics and network topology. We further show that many networked systems can exhibit similar coherent behavior by establishing a concentration result in a setting with randomly chosen individual nodal dynamics.
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大规模紧密连接网络的动力学集中
DOI：
10.1109/cdc40024.2019.9029796
发表时间：
2019
期刊：
Conference on Decision and Control
影响因子：
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作者：
Min, Hancheng;Mallada, Enrique
通讯作者：
Mallada, Enrique
DOI：
10.1109/cdc.2017.8263893
发表时间：
2017-12
期刊：
2017 IEEE 56th Annual Conference on Decision and Control (CDC)
影响因子：
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作者：
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通讯作者：
Hasan Giray Oral;Enrique Mallada;D. Gayme
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DOI：
10.1109/cdc.2017.8264414
发表时间：
2017
期刊：
56th IEEE Conference on Decision and Control (CDC
影响因子：
--
作者：
Jiang, Yan;Pates, Richard;Mallada, Enrique
通讯作者：
Mallada, Enrique
低惯量电力系统的电网形成频率整形控制
DOI：
10.23919/acc50511.2021.9482678
发表时间：
2021
期刊：
American Control Conference
影响因子：
--
作者：
Jiang, Yan;Bernstein, Andrey;Vorobev, Petr;Mallada, Enrique
通讯作者：
Mallada, Enrique
影响因子：
3
作者：
Min, Hancheng;Paganini, Fernando;Mallada, Enrique
通讯作者：
Mallada, Enrique